All categories

4 years ago

SteelDrivers 78 miles on 3 gallons of gas find the miles per gallon

Mathematics

1 answer:

Neko [114]4 years ago

4 0

78 divided by 3 = 25

You might be interested in

Express in scientific notation. Make sure your answer has the same number of significant figures as the starting value.

Elenna [48]

Answer:

1.325 x 10 -2

Step-by-step explanation:

That is the answer and I know 100% that it is correct

7 0

3 years ago

A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and top, and a volume of 44 cm3.

Maurinko [17]

Answer:

Base= 5.09 cm x 5.09 cm; height = 1.69 cm

Step-by-step explanation:

-> materials has a square base of side length, dimension will be: x . x = x²

'y' represents height

->For dimensions of 4 silver plated sides= xy each

->dimensions of the nickel plated top= x²

Volume = yx²

44=yx² => y= 44/x²

Cost of the sides will be( 4 * xy * $3 )

Cost of the top and the bottom will be (2 * x² * $1)

For the Total cost: 12xy + 2x²

substituting value of 'y' in above equation,

=> Total cost = 12x (44/x²) + 2x² = 528 / x + 2x²

To Minimum critical point => d [cost] / dx = 0

=> - 528/x² + 4x =0

132/x² - x =0

132 - x³ = 0

x³ = 132

Taking cube root on both sides

∛x³ = ∛(132)

x= 5.09

=> y = 44/5.09² =>1.69

Dimensions of the box :

Base= 5.09 cm x 5.09 cm; height = 1.69 cm

4 0

3 years ago

Radical functions. please help me!

Sphinxa [80]

These are 8 questions and 8 answers:

1) Quesion 1:

9+√2
---------
4 - √7

Answer: the third option:

36 + 9√7 + 4√2 + √14
-----------------------------
9

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator.

The conjugate of 4 - √7 = 4 + √7

=>

$\frac{9+ \sqrt{2} }{4- \sqrt{7} } . \frac{4+ \sqrt{7} }{4+ \sqrt{7} } = \frac{(9)(4)+9 \sqrt{7}+4 \sqrt{2} + \sqrt{2} . \sqrt{7} }{(4)^2-( \sqrt{7})^2 } =$

$= \frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14} }{16-7}$

2) Question 2: sum

$5x (\sqrt[3]{x^2y})+2( \sqrt[3]{x^5y})$

Answer: fourth option

$7x( \sqrt[3]{x^2y} )$

Explanation:

Take x^5 out of the second radical which will result in a like term of the first radical:

$5x( \sqrt[3]{x^2y} )+2( \sqrt[3]{x^5y}) =5x( \sqrt[3]{x^2y} )+2x( \sqrt[3]{x^2y})=7x( \sqrt[3]{x^2y})$

which is the fourth option

3) Question 3. Which expression is equivalent to:

$\frac{ \sqrt{10} }{ \sqrt[4]{8} }$

Answer: the first option

Explanation

$\frac{ \sqrt{10} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{10^2} }{ \sqrt[4]{8} } = \frac{ \sqrt[4]{100} }{ \sqrt[4]{8} } . \frac{ \sqrt[4]{8^3} }{ \sqrt[4]{8^3} } = \frac{ \sqrt[4]{(100)(512)} }{8} = \frac{ \sqrt[4]{51200} }{8} = \frac{4 \sqrt[4]{200} }{8} = \frac{ \sqrt[4]{200} }{2}$

4) Question 4 What is the simplest form?

Answer: the second option

Explanation:

$\sqrt[4]{81x^8y^5}=x^2 y\sqrt[4]{3^4y} =3x^2y \sqrt[4]{y}$

5) Question 5 Product

Answer: the fourth option:

$104x^4+16x^4 \sqrt{30} [/tex]\\Explanation:\\Use the square of a binomial product: (a + b)^2 = a^2 + 2ab + b^2\\[tex](4x \sqrt{5x^2} )^2+2(4x \sqrt{5x^2})(2x^2 \sqrt{6}) +(2x^2 \sqrt{6} )^2=$

$=16x^2(5x^2)+16x^4( \sqrt{30} )+4x^4(6)=80x^4+16x^4 \sqrt{30} +24x^4=$

$=104x^4+16x^4 \sqrt{30}$

which is the fourth option.

6) Question 6 Product

Answer: fourth option

Explanation:

$\sqrt[3]{16x^7} . \sqrt[3]{12x^9} = \sqrt[3]{2^4.2^2.3x^7x^9} = \sqrt[3]{2^6.3.x^{16}}=2^2 x^5 \sqrt[3]{3x} =4 x^5\sqrt[3]{3x}$

which is the fourth option.

7) Question 7. Simplified form of 2√18 + 3√2 + √162

Answer: 18√2

Explanation:

$2 \sqrt{18}+3 \sqrt{2} + \sqrt{162}=2(3) \sqrt{2} + 3 \sqrt{2} +9 \sqrt{2} =18 \sqrt{2}$

which is the second option.

8) Question 8 which function is undefined for x = 0.

Answer: second option y = √ (x - 2)

Explanation.

The square root function is not defined for negative values.

When x = 0, x - 2 = -2, whose square root is not defined.

Therefore, the square root of x - 2 is not defined for x = 0.